I second Lastminute.com, we used them for our london Hotel a couple of months ago, and there's loads of good deals.
If you're feeling adventurous you could even try their 'Top Secret' hotels, they tell you the approximate area and the star rating, but not the name. But they give you really great deals for taking the risk. I didn't try it this time, but I will definately next time.
We stayed in the Hyde Park Corus, we went to a show, but we did have to take the tube to get to the West End. But I'm sure you'll find lots actually in the area you want.
Have a great time.